TORONTO/CAIRO (Reuters) - Canadian police said on Wednesday that they had no evidence so far to support claims by the Islamic State militant group that it was responsible for a weekend shooting in Toronto that left two people dead and 13 wounded.

Faisal Hussain, 29, was identified by police as the gunman who opened fire on a busy Toronto street, killing 10-year-old girl Julianna Kozis and 18-year-old Reese Fallon. He was found dead shortly afterwards, authorities said.

Hussain, buried by his family on Wednesday morning, died of a self-inflicted gunshot wound, a source close to the family said. The Special Investigations Unit, an independent body looking into his demise, would not confirm a cause of death.

Islamic State said through its AMAQ news agency that Hussain "was a soldier of the Islamic State and carried out the attack in response to calls to target the citizens of the coalition countries." It did not provide evidence for its claim.

"At this stage, we have no evidence to support these claims," said Toronto Police Chief Mark Saunders.

"We will continue to explore every investigative avenue including interviewing those who knew Mr. Hussain, reviewing his online activity, and looking into his experiences with mental health."

Hussain's family said he worked in a grocery store but spent much of his time at home, and the struggled with severe mental illness.

Police said it was not known how Hussain obtained a gun.

The Canadian Broadcasting Corporation, citing an unnamed police source, reported on Wednesday that Hussain got the gun from his brother, Fahad Hussain, and that it had been traced to the United States.

(Reporting by Omar Fahmy in Cairo and Danya Hajjaji and Anna Mehler Paperny in Toronto; Editing by John Stonestreet and Susan Thomas)